Question: Express this quotient in scientific notation: ${\frac{3.010\times 10^{9}} {7.0\times 10^{5}}}$
Start by collecting like terms together. $= {\frac{3.010} {7.0}} \times{\frac{10^{9}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.43 \times 10^{9\,-\,5}$ $= 0.43 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.43$ is the same as $4.30 \div 10$ , or $4.30 \times 10^{-1}$ $ = {4.30 \times 10^{-1}} \times 10^{4} $ $= 4.30\times 10^{3}$